After an injury (broken collarbone, shoulder blade and rib) last year I'm trying to get back up to strength. It's several months since I was cleared to resume normal exercise, so this question is about rebuilding strength rather than injury recovery. While I'm weaker overall than before the exercise, the side I injured has obviously lost more strength than the other side, not helped by it being my non-dominant side I broke. I'm interested in general strength training, rather than bodybuilding or serious lifting - I'm more into cycling and kayaking. The latter in particular benefits from reasonable upper-body strength even if the power comes from lower down.
For many exercises I can do drop sets, extra sets, or even a short extra session on the weak side only (shoulder press, many bicep exercises, shoulder raises, bench rows), but I'm noticing that I can't get back to a more than 1 or 2 wide-grip pull-ups, even though I can do a couple of one-hand pull-ups on the weak side with the other hand gripping my wrist. Anything I've tried (e.g. pull-down machine with various grips) seems to end up working the biceps rather than lats. All the pull-down stations at my gym are pulley- rather than lever-based, which I normally prefer; otherwise the gym is fairly well-equipped.
So how can I rebuild lat strength on the side that's lost it?